Recent work on measuring growth with categorical outcome variables has combined the item response theory (IRT) measurement model with the latent growth curve model and extended the assessment of growth to multidimensional IRT models and higher order IRT models. However, there is a lack of synthetic studies that clearly evaluate the strength and…

With this article, we propose using a Bayesian multilevel latent class (BMLC; or mixture) model for the multiple imputation of nested categorical data. Unlike recently developed methods that can only pick up associations between pairs of variables, the multilevel mixture model we propose is flexible enough to automatically deal with complex…

Cluster analysis is a set of statistical methods for discovering new group/class structure when exploring data sets. This article reviews the following popular libraries/commands in the R software language for applying different types of cluster analysis: from the stats library, the kmeans, and hclust functions; the mclust library; the poLCA…

Multiple imputation (MI) can be used to address missing data at Level 2 in multilevel research. In this article, we compare joint modeling (JM) and the fully conditional specification (FCS) of MI as well as different strategies for including auxiliary variables at Level 1 using either their manifest or their latent cluster means. We show with…

In a traditional regression-discontinuity design (RDD), units are assigned to treatment on the basis of a cutoff score and a continuous assignment variable. The treatment effect is measured at a single cutoff location along the assignment variable. This article introduces the multivariate regression-discontinuity design (MRDD), where multiple…

Dominance analysis (DA) is a method used to compare the relative importance of predictors in multiple regression. DA determines the dominance of one predictor over another by comparing their additional R[squared] contributions across all subset models. In this article DA is extended to multivariate models by identifying a minimal set of criteria…

Provides power comparisons for three permutation tests and the Bartlett-Nanda-Pillai trace test (BNP) (M. Bartlett, 1939; D. Nanda, 1950; K. Pillai, 1955) in completely randomized experimental designs with correlated multivariate-dependent variables. The power of the BNP was generally found to be less than that of at least one of the permutation…